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Identity:
Example:
Expand \(27x^3 + 8y^3 + z^3 - 18xyz\).
Solution:
Let us write the expression of \(27x^3 + 8y^3 + z^3 - 18xyz\) using the identity .
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Important!
If then the identity is rewritten as follows:
Example:
Evaluate \(8^3 - 5^3 - 3^3\).
Solution:
By the identity if , then .
On comparing \(8^3 - 5^3 - 3^3\) with we have \(a\) \(=\) \(8\), \(b\) \(=\) \(5\) and \(c\) \(=\) \(3\).
Here \(a+b+c\) \(=\) \(8-5-3\) \(=\) \(0\)
Therefore, \(8^3 - 5^3 - 3^3\) \(=\) \(3 \times 8 \times 5 \times 3\) \(=\) \(360\)